/* linbox/solutions/minpoly.h
 * Copyright (C) 1999, 2001 Jean-Guillaume Dumas
 *
 * Written by Jean-Guillaume Dumas <Jean-Guillaume.Dumas@imag.fr>
 *
 * ========LICENCE========
 * This file is part of the library LinBox.
 *
  * LinBox is free software: you can redistribute it and/or modify
 * it under the terms of the  GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 * ========LICENCE========
 */

#ifndef __LINBOX_minpoly_H
#define __LINBOX_minpoly_H

#include <string>
#include "linbox/linbox-config.h"
#include "linbox/solutions/methods.h"
#include "linbox/util/commentator.h"

#include "linbox/blackbox/squarize.h"

#include "linbox/matrix/matrix-domain.h"
#include "linbox/algorithms/wiedemann.h"
#include "linbox/solutions/hadamard-bound.h"

#ifdef __LINBOX_HAVE_MPI
#include "linbox/util/mpicpp.h"
#include "linbox/algorithms/cra-distributed.h"
#endif

#include "linbox/algorithms/minpoly-integer.h"

namespace LinBox
{

	/*! @internal
	 * @brief Minimal polynomial of a blackbox linear operator A.
	 * The resulting polynomial is a vector of coefficients.
	 * Somewhere we should document our handling of polys.
	 */
	template < class Blackbox, class Polynomial, class DomainCategory, class MyMethod>
	Polynomial &minpoly (Polynomial           & P,
			     const Blackbox       & A,
			     const DomainCategory & tag,
			     const MyMethod       & M);

	/*
	   template < class Blackbox, class Polynomial, class MyMethod>
	   Polynomial &minpoly (Polynomial& P,
	   const Blackbox& A,
	   const RingCategories::RationalTag& tag,
	   const MyMethod& M)
	   {
	   throw LinboxError("LinBox ERROR: minpoly is not yet defined over a rational domain");
	   }
	   */

	/** @internal
	 * \brief  ...using an optional Method parameter
	 * \param P  the output minimal polynomial.  If the polynomial is
	 * of degree d, this random access container has size d+1, the 0-th entry is
	 * the constant coefficient and the d-th is 1 since the minpoly is monic.
	 * \param A  a blackbox matrix
	 * \param M  the method object.  Generally, the default
	 * object suffices and the algorithm used is determined by the class of M.
	 * Basic methods are Method::Blackbox, Method::Elimination, and Method::Auto
	 * (the default).
	 * See methods.h for more options.
	 * \return a reference to P.
	  */
	template < class Blackbox, class Polynomial, class MyMethod>
	Polynomial &minpoly (Polynomial     & P,
			     const Blackbox & A,
			     const MyMethod & M)
	{
		return minpoly (P, A, typename FieldTraits<typename Blackbox::Field>::categoryTag(), M);
	}

	/// \brief  ...using default Method
	template<class Polynomial, class Blackbox>
	Polynomial &minpoly (Polynomial     &P,
			     const Blackbox &A)
	{
		return minpoly (P, A, Method::Auto());
	}



	//! @internal The minpoly with Auto Method
	template<class Polynomial, class Blackbox>
	Polynomial &minpoly (
			     Polynomial                       & P,
			     const Blackbox                   & A,
			     const RingCategories::ModularTag & tag,
			     const Method::Auto             & M)
	{
		return minpoly(P, A, tag, Method::Blackbox(M));
	}

	//! @internal The minpoly with Auto Method on BlasMatrix
	template<class Polynomial, class Field>
	Polynomial &minpoly (
			     Polynomial                       & P,
			     const BlasMatrix<Field>          & A,
			     const RingCategories::ModularTag & tag,
			     const Method::Auto             & M)
	{
		return minpoly(P, A, tag, Method::Elimination(M));
	}

	//! @internal The minpoly with Elimination Method
	template<class Polynomial, class Blackbox>
	Polynomial &minpoly (
			     Polynomial                       & P,
			     const Blackbox                   & A,
			     const RingCategories::ModularTag & tag,
			     const Method::Elimination        & M)
	{
		return minpoly(P, A, tag, Method::DenseElimination(M));
	}

	//! @internal The minpoly with DenseElimination Method
	template<class Polynomial, class Blackbox>
	Polynomial &minpoly (
			     Polynomial                       & P,
			     const Blackbox                   & A,
			     const RingCategories::ModularTag & tag,
			     const Method::DenseElimination    & M)
	{
		commentator().start ("Convertion to BLAS Minimal polynomial", "blasconvert");

		if (A.coldim() != A.rowdim()) {
			commentator().report(Commentator::LEVEL_IMPORTANT, INTERNAL_DESCRIPTION) << "Squarize matrix" << std::endl;
			Squarize<Blackbox> B(&A);
			BlasMatrix< typename Blackbox::Field > BBB (B);
			BlasMatrixDomain< typename Blackbox::Field > BMD (BBB.field());
			commentator().stop ("done", NULL, "blasconvert");

			return BMD.minpoly (P, static_cast<const BlasMatrix<typename Blackbox::Field>& >(BBB));
		}
		else {
			BlasMatrix< typename Blackbox::Field > BBB (A);
			BlasMatrixDomain< typename Blackbox::Field > BMD (BBB.field());
			commentator().stop ("done", NULL, "blasconvert");
                        return BMD.minpoly (P, static_cast<const BlasMatrix<typename Blackbox::Field>& >(BBB));
		}
	}

	//! @internal The minpoly with BlackBox Method
	template<class Polynomial, class Blackbox>
	Polynomial &minpoly (
			     Polynomial                       & P,
			     const Blackbox                   & A,
			     const RingCategories::ModularTag & tag,
			     const Method::Blackbox           & M)
	{
		if (M.certifyInconsistency) {
			// Will make a word size extension
			// when field size is too small
			minpoly(P, A, tag, Method::WiedemannExtension (M));
			return P;
		}
		else
			return minpoly(P, A, tag, Method::Wiedemann (M));
	}



}

// ---------------------------------------------------------
// Chinese Remaindering generic wrappers for integer minpoly
// ---------------------------------------------------------

#include "linbox/ring/modular.h"
#include "linbox/algorithms/cra-domain.h"
#include "linbox/randiter/random-prime.h"
#include "linbox/algorithms/matrix-hom.h"

#include "linbox/algorithms/rational-cra-var-prec.h"
#include "linbox/algorithms/cra-builder-var-prec-early-multip.h"
#include "linbox/algorithms/minpoly-rational.h"

namespace LinBox
{

	template <class Blackbox, class MyMethod>
	struct IntegerModularMinpoly {
		const Blackbox &A;
		const MyMethod &M;

		IntegerModularMinpoly(const Blackbox& b, const MyMethod& n) :
			A(b), M(n)
		{}


		template<typename Polynomial, typename Field>
		IterationResult operator()(Polynomial& P, const Field& F) const
		{
			typedef typename Blackbox::template rebind<Field>::other FBlackbox;
			FBlackbox Ap(A, F);
			minpoly( P, Ap, typename FieldTraits<Field>::categoryTag(), M);
			return IterationResult::CONTINUE;
		}
	};

	template <class Polynomial, class Blackbox, class MyMethod>
	Polynomial &minpoly (Polynomial 			&P,
                         const Blackbox                     &A,
                         const RingCategories::IntegerTag   &tag,
                         const MyMethod                     &M)
	{
        if (A.rowdim() == 0 || A.coldim() == 0){
            P.resize(1);
            P.field().assign(P[0],P.field().one);
            return P;
        }
#if 0
		if (A.coldim() != A.rowdim())
			throw LinboxError("LinBox ERROR: matrix must be square for minimal polynomial computation\n");
#endif

#ifdef __LINBOX_HAVE_MPI
		Communicator *c = M.pCommunicator;
		if(!c || c->rank() == 0)
			commentator().start ("Integer Minpoly", "Iminpoly");
		else{
                //commentator().setMaxDepth(0);
                //commentator().setMaxDetailLevel(0);
                //commentator().setPrintParameters(0, 0, 0);
		}
#else
		commentator().start ("Integer Minpoly", "Iminpoly");
#endif
            // 0.7213475205 is an upper approximation of 1/(2log(2))
		typedef Givaro::ModularBalanced<double> Field;
        PrimeIterator<IteratorCategories::HeuristicTag> genprime(FieldTraits<Field>::bestBitSize(A.coldim()));
		IntegerModularMinpoly<Blackbox,MyMethod> iteration(A, M);

            // @todo: use a value for the switch provided by the method and not by a macro
#  ifdef __LINBOX_HEURISTIC_CRA
		ChineseRemainder< CRABuilderEarlyMultip<Field > > cra(LINBOX_DEFAULT_EARLY_TERMINATION_THRESHOLD);
#  else
        double hbound = FastCharPolyHadamardBound(A);
		ChineseRemainder< CRABuilderFullMultip<Field > > cra(hbound);
#  endif
		cra(P, iteration, genprime);

#ifdef __LINBOX_HAVE_MPI
		if(!c || c->rank() == 0)
#endif
			commentator().stop ("done", NULL, "Iminpoly");
		return P;
	}

	template < class Blackbox, class Polynomial, class MyMethod>
	Polynomial &minpoly (Polynomial                        & P,
			     const Blackbox                    & A,
			     const RingCategories::RationalTag & tag,
			     const MyMethod                    & M)
	{
		commentator().start ("Rational Minpoly", "Rminpoly");

		typedef Givaro::ModularBalanced<double> Field;
                PrimeIterator<IteratorCategories::HeuristicTag> genprime(FieldTraits<Field>::bestBitSize(A.coldim()));
		RationalChineseRemainderVarPrec< CRABuilderVarPrecEarlyMultip<Field> > rra(LINBOX_DEFAULT_EARLY_TERMINATION_THRESHOLD);
		IntegerModularMinpoly<Blackbox,MyMethod> iteration(A, M);

		std::vector<Integer> PP; // use of integer due to non genericity of cra. PG 2005-08-04
		Integer den;
		rra(PP,den, iteration, genprime);
		size_t i =0;
		P.resize(PP.size());
		for (typename Polynomial::iterator it= P.begin(); it != P.end(); ++it, ++i)
			A.field().init(*it, PP[i],den);

		commentator().stop ("done", NULL, "Rminpoly");

		return P;
	}

	template < class Field, template<class> class Polynomial, class MyMethod>
	Polynomial<typename Field::Element> &minpoly (Polynomial<typename Field::Element>& P,
						      const BlasMatrix<Field>            & A,
						      const RingCategories::RationalTag  & tag,
						      const MyMethod                     & M)
	{
		commentator().start ("Dense Rational Minpoly", "Rminpoly");

		rational_minpoly(P,A,M);
		return P;
	}

} // end of LinBox namespace
#endif // __LINBOX_minpoly_H

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